The arrow of time (again)

[TheHutch]

TL;DR

Why does everyone keep saying that all the laws of physics are time reversible?

I am forever seeing claims that the laws of physics are symmetrical in time, so to explain the 'arrow of time' we have to resort to statistical effects - increasing entropy and so on.
But isn't there one law that is manifestly not time reversible: wave function collapse, or its equivalent in many-worlds formulations?
What am I missing? (I did scan previous threads before posting this, but they all seem to discuss entropy)

 

[PeroK]

Good question. There's a discussion here:

https://physics.stackexchange.com/questions/359799/why-is-quantum-mechanics-reversible

 

[anuttarasammyak]

TL;DR Summary: Why does everyone keep saying that all the laws of physics are time reversible?

But isn't there one law that is manifestly not time reversible: wave function collapse, or its equivalent in many-worlds formulations?

Long years ago Landau Lifshitz Statistical Mechanics says conjecture that entropy increase law comes from it. I don’t know how the current physics deals with it.

 

[PeterDonis]

But isn't there one law that is manifestly not time reversible: wave function collapse

Wave function collapse is not a law in QM--it's a hand-waving process for computing probabilities for follow-on measurements without having to commit oneself to any claims about what is "really going on" behind the scenes. It is true that, mathematically, the operation involved is not reversible. But that operation is not claimed to correspond to anything "real". It's just a mathematical calculation.

or its equivalent in many-worlds formulations?

The equivalent of "wave function collapse" in the MWI also does not correspond to anything "real" and is just a mathematical calculation--the MWI makes that starkly evident by saying that all the other branches of the wave function are still there, so the only actual "law" in the MWI is unitary evolution of the wave function of the entire universe, which is manifestly time reversible.

 

[Demystifier]

According to the Copenhagen interpretation, the wave function collapses when a measurement is performed, where measurement is described by classical physics. But classical physics is fundamentally time reversible, it only looks irreversible at the macroscopic level due to statistical reasons. Hence, if we take Copenhagen interpretation seriously, the collapse must also be something that only looks irreversible at the macroscopic level due to statistical reasons.

Or if you don't buy Copenhagen interpretation, but still believe in some kind of collapse, you must specify more precisely how and when the wave function collapses. It is only after you specify it that you can answer the question whether the collapse violates time reversibility or not. In particular, in MWI, the collapse is an illusion appearing only at the macroscopic level, so violation of time reversibility due to collapse is also an illusion appearing only at the macroscopic level.

 

[Albertus Magnus]

Wave function collapse is not a law in QM--it's a hand-waving process for computing probabilities for follow-on measurements without having to commit oneself to any claims about what is "really going on" behind the scenes. It is true that, mathematically, the operation involved is not reversible. But that operation is not claimed to correspond to anything "real". It's just a mathematical calculation.


The equivalent of "wave function collapse" in the MWI also does not correspond to anything "real" and is just a mathematical calculation--the MWI makes that starkly evident by saying that all the other branches of the wave function are still there, so the only actual "law" in the MWI is unitary evolution of the wave function of the entire universe, which is manifestly time reversible.

How does one know what is real apart from the models one uses to make sense of observation? Perhaps, the only things that are real are the observations?

 

[PeterDonis]

How does one know what is real apart from the models one uses to make sense of observation?

QM interpretations are models, which make specific claims about what is "real" and what isn't. Their claims are mutually inconsistent, which is why QM interpretation remains an active area of controversy even after a century.

Perhaps, the only things that are real are the observations?

Perhaps. Indeed, that's one definition of "real" that some people use. But it's certainly not the only one. If it were, there would not be multiple interpretations of QM that are inconsistent with each other, for one thing.

 

[Pythagorean]

• I wonder if you can really define arrow of time without thermodynamics or expansion of universe.
• is 2nd law really just statistical?
  • Prigogine didn't think so and that led to a theory of dissipative structures.
  • dispersion and irreversibility are classical and deterministic
• The observer in wave function collapse reminds me a lot of Maxwell's Demon.

 

[TheHutch]

Thanks everyone for the replies, it takes a little digesting... I'm not sure I'm following the Lindblad equation, for example. But here are some follow-on observations and questions:

Wave function collapse is not a law in QM--it's a hand-waving process for computing probabilities

Don't mathematical formulations that make predictions that agree with observations have a right to be called 'laws'? Is the argument that they also have to be deterministic? I know collapse is a bit controversial, but it does make accurate predictions and surely something 'real' is happening if a superposition of photon states transforms into a 'photon detected at position x' state? (even if one thinks the superposition isn't 'real' it surely reflects something that is real, otherwise the calculations wouldn't work).

That said, I'm not a great fan of the Copenhagen interpretation, Gott würfelt nicht! and all that. I find a many worlds formulation more intellectually appealing, and it is, as far as I understand it, deterministic - all outcomes occur, one superposition leads to another grand superposition with (perhaps?) no loss of information.

the only actual "law" in the MWI is unitary evolution of the wave function of the entire universe, which is manifestly time reversible

In particular, in MWI, the collapse is an illusion appearing only at the macroscopic level, so violation of time reversibility due to collapse is also an illusion appearing only at the macroscopic level.

Now, again as I see it, in MWI our photon superposition leads to a superposition of 'photon detected at x' states. We poor mortals can only be aware of one of these states, (don't worry, I don't think consciousness is required here - the detector is in a similar position), but again, something irreversible has happened in the local context, which is what I think Demystifier meant by 'the macroscopic level'. Since the universal wave function is a superposition of these macroscopic levels, does that not imply that a collection of arrows of time, all pointing in the same direction at the macroscopic level, will define an overall arrow of time at the universal level? Or are we saying that no loss of information implies no arrow of time? Isn't our whole aim to prise apart direction of time from statistical or informational considerations?

 

[PeterDonis]

Don't mathematical formulations that make predictions that agree with observations have a right to be called 'laws'?

Wave function collapse isn't a "mathematical formulation". It's just an ad hoc rule, with no justification except that it allows us to make correct predictions. But the ad hoc rule does not tell you, from first principles, when to apply it--it doesn't give any mathematical formulation for when collapse happens. All it says is to apply the collapse rule whenever it works to make correct predictions. That's not a "law". It's a stopgap while physicists try to figure out something better.

Is the argument that they also have to be deterministic?

Many physicists are uncomfortable with calling probabilistic rules "laws", yes. But I don't think that's the primary issue with collapse. See above.

surely something 'real' is happening if a superposition of photon states transforms into a 'photon detected at position x' state?

This never happens.

First, photons are a very poor choice for this kind of analysis, since they do not even have "position" states (for the gory technical details, look up "Newton-Wigner localization" and why it doesn't work for photons).

Second, no actual detection of any particle is "at position x". There are always finite error bars. Using exact position states is an idealization for pedagogical purposes. It does not reflect anything in an actual experiment.

in MWI our photon superposition leads to a superposition of 'photon detected at x' states.

No, that's not quite what happens. I'll describe what does happen, according to the MWI, below. Instead of "photon" I'll just say "particle" and assume that we're hand-waving away any issues with localization.

Then, if we have a particle whose state is not an eigenstate of position, and we measure its position, what the MWI says we are actually doing is entangling the particle with the measuring apparatus. So we end up with an entangled state that is a sum of products of kets of the form

$$
\ket{\text{particle at position x}} \ket{\text{measuring device detects particle at position x}}
$$

(where in a real experiment "at position x" would be replaced with "somewhere in finite-sized position bucket x"). The sum is over all possible positions (or position buckets) that can be detected in the experiment.

something irreversible has happened in the local context

Something apparently irreversible happens in the local context. But the apparent irreversibility is only because the "local context" doesn't see the entire state. It only sees one piece of it. Apparent irreversibility due to ignorance of the complete state is a standard thing in thermodynamics. The apparent irreversibility would disappear if the full state were known; the dynamics of the full state is reversible (in the case of QM, it's unitary, which is reversible).

the universal wave function is a superposition of these macroscopic levels

Not in the sense you mean. You can't deduce from the fact that each local context is apparently irreversible, that the universal wave function's dynamics are irreversible. That's simply not a valid deduction. It's wrong.

 

[PeterDonis]

Isn't our whole aim to prise apart direction of time from statistical or informational considerations?

I don't know what your whole aim is. But as I understand it, the standard view in physics is that you can't separate arrows of time from statistical or informational considerations, since the latter are where the apparent irreversibility that causes us to perceive an arrow of time comes from.

Of course it's possible in principle that we're wrong about the underlying dynamics of the complete state (the universal wave function in MWI-speak), and that it actually is irreversible fundamentally, so the irreversibility we see in our "local context" is not just apparent. But nobody has any evidence for this, and nobody has any ideas about how to test it experimentally. So it's just speculation at this point.

 

[Pythagorean]

I don't want to hurt QM's feelings, but I think it's incomplete - particularly as any kind of description of spacetime.

 

[PeterDonis]

particularly as any kind of description of spacetime.

Note that if you want a quantum theory that is consistent with a spacetime description, you need to be looking at quantum field theory, not non-relativistic QM.

 

[Demystifier]

Now, again as I see it, in MWI our photon superposition leads to a superposition of 'photon detected at x' states. We poor mortals can only be aware of one of these states, (don't worry, I don't think consciousness is required here - the detector is in a similar position), but again, something irreversible has happened in the local context, which is what I think Demystifier meant by 'the macroscopic level'. Since the universal wave function is a superposition of these macroscopic levels, does that not imply that a collection of arrows of time, all pointing in the same direction at the macroscopic level, will define an overall arrow of time at the universal level? Or are we saying that no loss of information implies no arrow of time? Isn't our whole aim to prise apart direction of time from statistical or informational considerations?

Do you know what is decoherence? If you don't, I would suggest you to learn something about it, because it is a central part of QM needed to understand branching in MWI. In particular, to understand the time arrow in MWI, you must first understand the time arrow in decoherence. In short, decoherence explains branching, namely the increase of the number of branches over time. The fact that the number of branches is smaller in the past and larger in the future is nothing but the arrow of time in MWI.

 

[PeroK]

People are generally familiar with the idea that the process of mixing two liquids is theoretically reversible, but statistically almost impossible to reverse.

I guess it's less obvious that the processes in a macroscopic measuring device like the human eye are reversible. And theoretically the retina could emit several photons, which could reflect off a mirror and be absorbed by the filament in a light bulb.

The wave function collapse can be seen as our interpretation of the statistical irreversiblity of the macroscopic world as it affects our interactions with elementary physical processes, governed by QM.

 

[TheHutch]

Do you know what is decoherence? If you don't, I would suggest you to learn something about it, because it is a central part of QM needed to understand branching in MWI

Thanks for the tip, this should keep me quiet for a bit!

 

[Pythagorean]

Note that if you want a quantum theory that is consistent with a spacetime description, you need to be looking at quantum field theory, not non-relativistic QM.

I think that sort of demonstrates my point, that we smoosh QM with relativity and classical physics (since it's incomplete on its own) - and further, we still don't get an arrow of time. I know we can always patch different domains together in creative ways - quantum chaos, pchem, decoherence, field theory, etc. - and cross-interpret and parameterize curves. My point isn't to single QM out as more incomplete than other theories, just that it might not be most appropriate for understanding arrow of time.

 

[TheHutch]

Then, if we have a particle whose state is not an eigenstate of position, and we measure its position, what the MWI says we are actually doing is entangling the particle with the measuring apparatus.

I think this is what I was imagining earlier, when I referred to the MWI equivalent of wave function collapse. I think I have only ever heard of entanglement working one way in time - things become entangled but then stay entangled. Is that fair? The entanglement could perhaps get diluted to the point of invisibility by decoherence, but do we ever see two entangled particles coming together to become one non-entangled particle (the reverse of entangled pair generation)?

 

[PeterDonis]

things become entangled but then stay entangled.

That's not necessarily true. Entanglement is a unitary interaction, and any unitary interaction can be reversed. In quantum computing, there are gates that entangle two qubits, and gates that take two entangled qubits and un-entangle them. But doing that requires keeping very precise track of the states of each qubit.

When you start talking about systems containing large numbers of particles, it becomes impossible in any practical sense to un-entangle them once they're entangled, if you are using an interpretation like the MWI in which wave function collapse is not a real physical event. It's just not possible to keep track of the precise states of that many particles.